Operator Algebras

1. Front Matter

   Pages I-X

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2. Interpolation by Projections in C*-Algebras

   • Lawrence G. Brown, Gert K. Pedersen

   Pages 1-13

3. KMS States and Complex Multiplication (Part II)

   • Alain Connes, Matilde Marcolli, Niranjan Ramachandran

   Pages 15-59

4. An Algebraic Description of Boundary Maps Used in Index Theory

   • Joachim Cuntz

   Pages 61-86

5. On Rørdam's Classification of Certain C*-Algebras with One Non-Trivial Ideal

   • Søren Eilers, Gunnar Restorff

   Pages 87-96

6. Perturbation of Hausdorff Moment Sequences, and an Application to the Theory of C*-Algebras of Real Rank Zero

   • George A. Elliott, Mikael Rørdam

   Pages 97-115

7. Twisted K-Theory and Modular Invariants: I Quantum Doubles of Finite Groups

   • David E Evans

   Pages 117-144

8. The Orbit Structure of Cantor Minimal Z2-Systems

   • Thierry Giordano, Ian F. Putnam, Christian F. Skau

   Pages 145-160

9. Outer Actions of a Group on a Factor

   • Yoshikazu Katayama, Masamichi Takesaki

   Pages 161-163

10. Non-Separable AF-Algebras

    • Takeshi Katsura

    Pages 165-173

11. Central Sequences in C*-Algebras and Strongly Purely Infinite Algebras

    • Eberhard Kirchberg

    Pages 175-231

12. Lifting of an Asymptotically Inner Flow for a Separable C*-Algebra

    • Akitaka Kishimoto

    Pages 233-247

13. Remarks on Free Entropy Dimension

    • Dimitri Shlyakhtenko

    Pages 249-257

14. Notes on Treeability and Costs for Discrete Groupoids in Operator Algebra Framework

    • Yoshimichi Ueda

    Pages 259-279

The theme of this symposium was operator algebras in a wide sense. In the last 40 years operator algebras has developed from a rather special dis- pline within functional analysis to become a central ?eld in mathematics often described as “non-commutative geometry” (see for example the book “Non-Commutative Geometry” by the Fields medalist Alain Connes). It has branched out in several sub-disciplines and made contact with other subjects like for example mathematical physics, algebraic topology, geometry, dyn- ical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the ?rst symposium in the series of Abel Symposia to this group. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics re?ect to some extent how the subject has branched out. We are happy that some of the top researchers in the ?eld were willing to contribute. The basic ?eld of operator algebras is classi?ed within mathematics as part of functional analysis. Functional analysis treats analysis on in?nite - mensional spaces by using topological concepts. A linear map between two such spaces is called an operator. Examples are di?erential and integral - erators. An important feature is that the composition of two operators is a non-commutative operation.

• Algebra
• C*-algebra
• C*-algebras
• K-theory
• Minimum
• entropy
• functional analysis
• non-commutative geomtry
• operator algebras

• Department of Mathematics, University of Oslo, Oslo, Norway

  Ola Bratteli, Sergey Neshveyev

• Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

  Christian Skau

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